In 1998, Goldbach's Conjecture was shown by computer to be true for even numbers up to 400,000,000,000,000. In addition, some progress has been made towards formally proving the conjecture. As of this year, mathematicians with Goldbach fever have some extra incentive for their labours.

Up until the late 1990s, astronomers couldn't be certain that any planets existed outside our solar system. These days, not only are astronomers confident that planets are out there, but new ones are being discovered all the time.

In a major and expensive setback for NASA's Mars program, both the Mars Climate Orbiter and Mars Polar Lander spacecraft appear to have been lost. Soberingly, while the fate of the Mars Polar Lander is unclear, it appears that the Mars Climate Orbiter was lost due to a simple mathematical error.

Combining the computational powers of modern digital computers with the complex beauty of mathematical fractals has produced some entrancing artwork during the past two decades. Intriguingly, recent research at the University of New South Wales, Australia, has suggested that some works by the American artist Jackson Pollock also reflect a fractal structure.